This textbook provides the material for both basic and intermediate modern courses in dynamic analysis of ships and offshore structures. The word "modern" is used to signify that both deterministic and stochastic dynamics are covered. Because the main goal is to provide an introduction to dynamic analysis, the basic elements are described in some detail. A consequence of this is that the majority of the book deals with structures or structural elements that can be modeled or reduced to a single-degree-of-freedom (SDOF) system. However, realizing that multi-degree-offreedom (MDOF) systems are unavoidable in many practical situations the engineer is likely to meet, and, consequently, that the basic principles for their analysis should be understood, a chapter on linear MDOF systems is included. This is also done to clearly demonstrate the principle of modal decomposition whereby an MDOF system is reduced to a set of uncoupled SDOF systems.